Answer:
In the given figure the point on segment PQ is twice as from P as from Q is. What is the point? Ans is (2,1).
Step-by-step explanation:
There is really no need to use any quadratics or roots.
( Consider the same problem on the plain number line first. )
How do you find the number between 2 and 5 which is twice as far from 2 as from 5?
You take their difference, which is 3. Now splitting this distance by ratio 2:1 means the first distance is two thirds, the second is one third, so we get
4=2+23(5−2)
It works completely the same with geometric points (using vector operations), just linear interpolation: Call the result R, then
R=P+23(Q−P)
so in your case we get
R=(0,−1)+23(3,3)=(2,1)
Why does this work for 2D-distances as well, even if there seem to be roots involved? Because vector length behaves linearly after all! (meaning |t⋅a⃗ |=t|a⃗ | for any positive scalar t)
Edit: We'll try to divide a distance s into parts a and b such that a is twice as long as b. So it's a=2b and we get
s=a+b=2b+b=3b
⇔b=13s⇒a=23s
Midpoint formula
mid of (x1,y1) and (x2,y2) is
so
(22,15)=
therefor
22=
and
15=
slv each
22=
times both sides by 2
44=18+x1
minus 18 both sides
26=x1
15=
times both sides by 2
30=6+y1
minus 6
24=y1
the other point is (26,24)
Step-by-step explanation:
Area of triangular prism =1/2 ×base×height
550=1/2×22×h
h=550/11
h=50m
hope it helps.
Answer:
=
5
.
5
Step-by-step explanation:
